328 lines
8.7 KiB
C
328 lines
8.7 KiB
C
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/*
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* Copyright (c) 2003, 2007-14 Matteo Frigo
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* Copyright (c) 2003, 2007-14 Massachusetts Institute of Technology
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*
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*/
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#include "dft/dft.h"
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/*
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* Compute transforms of prime sizes using Rader's trick: turn them
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* into convolutions of size n - 1, which you then perform via a pair
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* of FFTs.
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*/
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typedef struct {
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solver super;
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} S;
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typedef struct {
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plan_dft super;
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plan *cld1, *cld2;
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R *omega;
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INT n, g, ginv;
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INT is, os;
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plan *cld_omega;
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} P;
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static rader_tl *omegas = 0;
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static R *mkomega(enum wakefulness wakefulness, plan *p_, INT n, INT ginv)
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{
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plan_dft *p = (plan_dft *) p_;
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R *omega;
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INT i, gpower;
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trigreal scale;
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triggen *t;
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if ((omega = X(rader_tl_find)(n, n, ginv, omegas)))
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return omega;
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omega = (R *)MALLOC(sizeof(R) * (n - 1) * 2, TWIDDLES);
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scale = n - 1.0; /* normalization for convolution */
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t = X(mktriggen)(wakefulness, n);
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for (i = 0, gpower = 1; i < n-1; ++i, gpower = MULMOD(gpower, ginv, n)) {
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trigreal w[2];
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t->cexpl(t, gpower, w);
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omega[2*i] = w[0] / scale;
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omega[2*i+1] = FFT_SIGN * w[1] / scale;
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}
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X(triggen_destroy)(t);
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A(gpower == 1);
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p->apply(p_, omega, omega + 1, omega, omega + 1);
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X(rader_tl_insert)(n, n, ginv, omega, &omegas);
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return omega;
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}
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static void free_omega(R *omega)
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{
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X(rader_tl_delete)(omega, &omegas);
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}
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/***************************************************************************/
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/* Below, we extensively use the identity that fft(x*)* = ifft(x) in
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order to share data between forward and backward transforms and to
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obviate the necessity of having separate forward and backward
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plans. (Although we often compute separate plans these days anyway
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due to the differing strides, etcetera.)
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Of course, since the new FFTW gives us separate pointers to
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the real and imaginary parts, we could have instead used the
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fft(r,i) = ifft(i,r) form of this identity, but it was easier to
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reuse the code from our old version. */
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static void apply(const plan *ego_, R *ri, R *ii, R *ro, R *io)
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{
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const P *ego = (const P *) ego_;
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INT is, os;
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INT k, gpower, g, r;
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R *buf;
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R r0 = ri[0], i0 = ii[0];
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r = ego->n; is = ego->is; os = ego->os; g = ego->g;
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buf = (R *) MALLOC(sizeof(R) * (r - 1) * 2, BUFFERS);
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/* First, permute the input, storing in buf: */
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for (gpower = 1, k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, g, r)) {
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R rA, iA;
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rA = ri[gpower * is];
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iA = ii[gpower * is];
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buf[2*k] = rA; buf[2*k + 1] = iA;
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}
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/* gpower == g^(r-1) mod r == 1 */;
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/* compute DFT of buf, storing in output (except DC): */
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{
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plan_dft *cld = (plan_dft *) ego->cld1;
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cld->apply(ego->cld1, buf, buf+1, ro+os, io+os);
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}
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/* set output DC component: */
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{
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ro[0] = r0 + ro[os];
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io[0] = i0 + io[os];
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}
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/* now, multiply by omega: */
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{
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const R *omega = ego->omega;
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for (k = 0; k < r - 1; ++k) {
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E rB, iB, rW, iW;
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rW = omega[2*k];
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iW = omega[2*k+1];
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rB = ro[(k+1)*os];
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iB = io[(k+1)*os];
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ro[(k+1)*os] = rW * rB - iW * iB;
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io[(k+1)*os] = -(rW * iB + iW * rB);
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}
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}
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/* this will add input[0] to all of the outputs after the ifft */
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ro[os] += r0;
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io[os] -= i0;
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/* inverse FFT: */
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{
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plan_dft *cld = (plan_dft *) ego->cld2;
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cld->apply(ego->cld2, ro+os, io+os, buf, buf+1);
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}
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/* finally, do inverse permutation to unshuffle the output: */
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{
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INT ginv = ego->ginv;
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gpower = 1;
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for (k = 0; k < r - 1; ++k, gpower = MULMOD(gpower, ginv, r)) {
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ro[gpower * os] = buf[2*k];
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io[gpower * os] = -buf[2*k+1];
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}
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A(gpower == 1);
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}
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X(ifree)(buf);
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}
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/***************************************************************************/
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static void awake(plan *ego_, enum wakefulness wakefulness)
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{
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P *ego = (P *) ego_;
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X(plan_awake)(ego->cld1, wakefulness);
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X(plan_awake)(ego->cld2, wakefulness);
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X(plan_awake)(ego->cld_omega, wakefulness);
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switch (wakefulness) {
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case SLEEPY:
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free_omega(ego->omega);
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ego->omega = 0;
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break;
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default:
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ego->g = X(find_generator)(ego->n);
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ego->ginv = X(power_mod)(ego->g, ego->n - 2, ego->n);
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A(MULMOD(ego->g, ego->ginv, ego->n) == 1);
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ego->omega = mkomega(wakefulness,
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ego->cld_omega, ego->n, ego->ginv);
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break;
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}
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}
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static void destroy(plan *ego_)
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{
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P *ego = (P *) ego_;
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X(plan_destroy_internal)(ego->cld_omega);
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X(plan_destroy_internal)(ego->cld2);
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X(plan_destroy_internal)(ego->cld1);
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}
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static void print(const plan *ego_, printer *p)
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{
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const P *ego = (const P *)ego_;
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p->print(p, "(dft-rader-%D%ois=%oos=%(%p%)",
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ego->n, ego->is, ego->os, ego->cld1);
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if (ego->cld2 != ego->cld1)
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p->print(p, "%(%p%)", ego->cld2);
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if (ego->cld_omega != ego->cld1 && ego->cld_omega != ego->cld2)
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p->print(p, "%(%p%)", ego->cld_omega);
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p->putchr(p, ')');
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}
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static int applicable(const solver *ego_, const problem *p_,
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const planner *plnr)
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{
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const problem_dft *p = (const problem_dft *) p_;
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UNUSED(ego_);
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return (1
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&& p->sz->rnk == 1
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&& p->vecsz->rnk == 0
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&& CIMPLIES(NO_SLOWP(plnr), p->sz->dims[0].n > RADER_MAX_SLOW)
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&& X(is_prime)(p->sz->dims[0].n)
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/* proclaim the solver SLOW if p-1 is not easily factorizable.
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Bluestein should take care of this case. */
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&& CIMPLIES(NO_SLOWP(plnr), X(factors_into_small_primes)(p->sz->dims[0].n - 1))
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);
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}
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static int mkP(P *pln, INT n, INT is, INT os, R *ro, R *io,
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planner *plnr)
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{
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plan *cld1 = (plan *) 0;
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plan *cld2 = (plan *) 0;
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plan *cld_omega = (plan *) 0;
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R *buf = (R *) 0;
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/* initial allocation for the purpose of planning */
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buf = (R *) MALLOC(sizeof(R) * (n - 1) * 2, BUFFERS);
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cld1 = X(mkplan_f_d)(plnr,
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X(mkproblem_dft_d)(X(mktensor_1d)(n - 1, 2, os),
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X(mktensor_1d)(1, 0, 0),
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buf, buf + 1, ro + os, io + os),
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NO_SLOW, 0, 0);
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if (!cld1) goto nada;
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cld2 = X(mkplan_f_d)(plnr,
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X(mkproblem_dft_d)(X(mktensor_1d)(n - 1, os, 2),
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X(mktensor_1d)(1, 0, 0),
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ro + os, io + os, buf, buf + 1),
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NO_SLOW, 0, 0);
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if (!cld2) goto nada;
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/* plan for omega array */
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cld_omega = X(mkplan_f_d)(plnr,
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X(mkproblem_dft_d)(X(mktensor_1d)(n - 1, 2, 2),
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X(mktensor_1d)(1, 0, 0),
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buf, buf + 1, buf, buf + 1),
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NO_SLOW, ESTIMATE, 0);
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if (!cld_omega) goto nada;
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/* deallocate buffers; let awake() or apply() allocate them for real */
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X(ifree)(buf);
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buf = 0;
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pln->cld1 = cld1;
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pln->cld2 = cld2;
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pln->cld_omega = cld_omega;
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pln->omega = 0;
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pln->n = n;
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pln->is = is;
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pln->os = os;
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X(ops_add)(&cld1->ops, &cld2->ops, &pln->super.super.ops);
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pln->super.super.ops.other += (n - 1) * (4 * 2 + 6) + 6;
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pln->super.super.ops.add += (n - 1) * 2 + 4;
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pln->super.super.ops.mul += (n - 1) * 4;
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return 1;
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nada:
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X(ifree0)(buf);
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X(plan_destroy_internal)(cld_omega);
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X(plan_destroy_internal)(cld2);
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X(plan_destroy_internal)(cld1);
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return 0;
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}
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static plan *mkplan(const solver *ego, const problem *p_, planner *plnr)
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{
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const problem_dft *p = (const problem_dft *) p_;
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P *pln;
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INT n;
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INT is, os;
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static const plan_adt padt = {
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X(dft_solve), awake, print, destroy
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};
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if (!applicable(ego, p_, plnr))
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return (plan *) 0;
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n = p->sz->dims[0].n;
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is = p->sz->dims[0].is;
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os = p->sz->dims[0].os;
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pln = MKPLAN_DFT(P, &padt, apply);
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if (!mkP(pln, n, is, os, p->ro, p->io, plnr)) {
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X(ifree)(pln);
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return (plan *) 0;
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}
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return &(pln->super.super);
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}
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static solver *mksolver(void)
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{
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static const solver_adt sadt = { PROBLEM_DFT, mkplan, 0 };
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S *slv = MKSOLVER(S, &sadt);
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return &(slv->super);
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}
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void X(dft_rader_register)(planner *p)
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{
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REGISTER_SOLVER(p, mksolver());
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}
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